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非线性分数阶微分方程边值问题正解的存在性和唯一性 被引量：2

Existence and Uniqueness of Positive Solutions for Boundary Value Problem of Nonlinear Fractional Differential Equation
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摘要 研究了非线性分数阶微分方程边值问题正解的存在性和唯一性,利用Schauder不动点定理得到了正解的存在性,利用Banach压缩映像原理得到了正解的唯一性. In this paper, we investigate the existence and uniqueness of positive solutions for a nonlinear boundary value problem of fractional differential equation. Using the Schauder fixed point theorem, we get the existence of positive solutions, and obtain uniqueness of positive solutions by using the banach contraction mapping theory.
作者 罗华 胡卫敏
机构地区 伊犁师范学院数学与统计学院
出处 《伊犁师范学院学报（自然科学版）》 2012年第4期1-7,共7页 Journal of Yili Normal University：Natural Science Edition
基金 新疆普通高校重点培育学科基金资助项目(XJZDXK2011004) 伊犁师范学院2012年度大学生课题(2012YJS010)
关键词 分数阶微分方程 正解 不动点 Fractional differential equation positive solutions fixed point
分类号 O175.1 [理学—基础数学]
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参考文献1

二级参考文献7

  • 1Bai Z B,Lü H S.Positive solutions for boundary value problem of nonlinear fractional differential equation,J Math Anal Appl,2005,311:495-505.
  • 2Zhang S Q.Positive solutions for boundary-value problems of nonlinear fractional differential equations,Electronic Journal of Differential Equations,2006,36:1-12.
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  • 7Schmitt K.A nonlinear boundary value problem,Journal of Differential Equations,1970,7:527-537.

共引文献9

同被引文献25

  • 1A A Killbas, Srivastava H M,Trujillo J J. Theory and Application of Fraction Differential Equation[M]. North-Holland Mathematic Studies 204, Amsterdam: Elsevier Science B V, 2006.
  • 2K B Oldham, J Spanier. The Fractional Calculus[M]. New York, London: Academic Press, 1974.
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  • 4S G Samko, A A Kilbas, O I Marichev. Fractional Integral and Derivatives (Theory and Application) IM]. Switzerland: Gordon and Breach, 1993.
  • 5Bai Z., Lv H. Positive solutions for boundary value problem of nonlinear fractional differential equation[J], J. Math. Anal.AppL, 2005, 311 : 495-505.
  • 6M EI-Shahed. Positive solutions for boundary value problems of nonlinear fractional differential equation[J]. Abstract and Applied Analysis, 2007, Article ID 10368, 8 pages, doi: 10.1155/2007/10368.
  • 7N Kosmatov. A singlar boundary value problem of nonlinear fractional differential equations of fractional order [J]. Journal of Applied Mathematics and Computing, 2008, 29(1): 125-135.
  • 8Li C F, Luo X N,Zhong Y. Existence of positive solutions of the boundary value problem for non-linear fractional differential equations[J]. Computers and Mathematics with Applications, 2010, 59: 1365-1375.
  • 9Wong F H. Existence of positive solutions of singular boundary value problems [J ]. Nonlinear Anal, 1993, 21: 397-406.
  • 10K S Ha, Y.H. Lee. Existence of multiple positive solutions of singular boundary value problems [J]. Nonlinear Anal, 1998, 28 37 -44.

引证文献2

二级引证文献5

伊犁师范学院学报（自然科学版）
2012年 第4期

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